Theorem 8 [1]}
Suppose that \(p>1\)  and \(1 / p+1 / q=1\) . If \(\mathcal {G}\)  and \(\mathcal {K}\)  are real functions on \([m_1, m_2]\)  such that \(|\mathcal {G}|^{p}\)  and \(|\mathcal {K}|^{q}\)  are integrable functions on \([m_1, m_2],\)  then
\(\int _{m_1}^{m_2}|\mathcal {G}(x) \mathcal {K}(x)| d x \le \left(\int _{m_1}^{m_2}|\mathcal {G}(x)|^{p} d x\right)^{\frac{1}{p}}\left(\int _{m_1}^{m_2}|\mathcal {K}(x)|^{q} d x\right)^{\frac{1}{q}}\) 
